This research was supported in part by Institute for Mathematics and its Applications
Finite element method, Galerkin methods, Multigrid methods (Numerical analysis)
A variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion problem, for which an error estimate is proved. A multigrid algorithm for this method is presented, and numerical experiments indicating its robustness with respect to diffusion coefficient are reported.
Published as: Gopalakrishnan, J., Kanschat, G. A multilevel discontinuous Galerkin method. Num. Math. 95, 527–550 (2003). https://doi.org/10.1007/s002110200392